where is fx x2ex Concave down Solutionfx 2xex x2ex fx 2e

where is f(x)= (x^2)(e^x) Concave down ?

f\'(x) = 2xe^x + x^2e^x

f\'\'(x) = 2e^x + 2xe^x + 2xe^x + x^2e^x

= 2e^x + 4xe^x + x^2e^x

f\'\'(x) < 0

2e^x + 4xe^x + x^2e^x < 0

Therefore

e^x(x^2 + 4x + 2) < 0

As e^x can\'t be less than 0

(x^2 + 4x + 2) < 0

-2 - 2 < x < 2 - 2

So (-2 - 2 , 2 - 2)

$where is f(x)= (x^2)(e^x) Concave down ? Solutionf\'(x) = 2xe^x + x^2e^x f\'\'(x) = 2e^x + 2xe^x + 2xe^x + x^2e^x = 2e^x + 4xe^x + x^2e^x f\'\'(x) < 0 2e^x +$

where is fx x2ex Concave down Solutionfx 2xex x2ex fx 2e

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